A transistor is operated in common emitter configuration at `V_(c)=2 V` such that a change in the base current from `100 muA` to `300 muA` produces a change in the collector current from `10 mA` to `20 mA`. The current gain is

Options

A. 25
B. 50
C. 75
D. 100

Answer

To find the current gain (β) of the transistor in a common emitter configuration, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the changes in base and collector currents:**
- The initial base current (IB1) = 100 µA = 100 × 10^(-6) A
- The final base current (IB2) = 300 µA = 300 × 10^(-6) A
- Change in base current (ΔIB) = IB2 - IB1 = 300 µA - 100 µA = 200 µA = 200 × 10^(-6) A

- The initial collector current (IC1) = 10 mA = 10 × 10^(-3) A
- The final collector current (IC2) = 20 mA = 20 × 10^(-3) A
- Change in collector current (ΔIC) = IC2 - IC1 = 20 mA - 10 mA = 10 mA = 10 × 10^(-3) A

2. **Calculate the current gain (β):**
- The current gain (β) is defined as the ratio of the change in collector current to the change in base current:
\[ \beta = \frac{\Delta IC}{\Delta IB} \]
- Substitute the values:
\[ \beta = \frac{10 \times 10^{-3}}{200 \times 10^{-6}} \]

3. **Perform the calculation:**
- Simplifying the fraction:
\[ \beta = \frac{10}{200} \times \frac{10^{-3}}{10^{-6}} = \frac{10}{200} \times 10^{3} \]
- This simplifies to:
\[ \beta = \frac{1}{20} \times 1000 = 50 \]

4. **Conclusion:**
- Therefore, the current gain (β) of the transistor is **50**.